CONTINUITY OF MULTIPLICATION IN THE LARGEST COMPACTIFICATION OF A LOCALLY COMPACT GROUP

Abstract

G[Lscr ][Uscr ][Cscr ] is the largest semigroup compactification of the locally compact group G. When G is not compact, given q ∈ G* = G[Lscr ][Uscr ][Cscr ] \ G, there is p ∈ G* such that x [map ] qx is discontinuous at p (Theorem 2). If G is σ-compact, there is one p which will serve for all q (Theorem 1).